New extension of beta, Gauss and confluent hypergeometric functions

Abstract

There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function 𝐵𝜁, 𝛼1 𝛼2; 𝑚1, 𝑚2 (𝑎1, 𝑎2) was introduced and presented here because of its important properties. The new extended Beta function has symmetric property, integral representations, Mellin transform, inverse Mellin transform and statistical properties like Beta distribution, mean, variance, moment and cumulative distribution which ware also presented. Finally, the new extended Gauss and Confluent Hypergeometric functions with their propertied were introduced and presented.